Quasi-semi-stable representations

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Fix K a p-adic field and denote by GK its absolute Galois group. Let K∞ be the extension of K obtained by adding pn-th roots of a fixed uniformizer, and G∞⊂GK its absolute Galois group. In this article, we define a class of p-adic torsion representations of G∞, calledquasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebraic objects. The results of this note should be considered as a first step in the understanding of the structure of quotient of two lattices in a crystalline (resp. semi-stable) Galois representation.

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@article{Caruso2009, abstract = {Fix $K$ a $p$-adic field and denote by $G_K$ its absolute Galois group. Let $K_\infty $ be the extension of $K$ obtained by adding $p^n$-th roots of a fixed uniformizer, and $G_\infty \subset G_K$ its absolute Galois group. In this article, we define a class of $p$-adic torsion representations of $G_\infty $, calledquasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebraic objects. The results of this note should be considered as a first step in the understanding of the structure of quotient of two lattices in a crystalline (resp. semi-stable) Galois representation.}, author = {Caruso, Xavier, Liu, Tong}, journal = {Bulletin de la Société Mathématique de France}, keywords = {torsion Galois representations; semi-stable representations; norm field theory}, language = {eng}, number = {2}, pages = {185-223}, publisher = {Société mathématique de France}, title = {Quasi-semi-stable representations}, url = {http://eudml.org/doc/272378}, volume = {137}, year = {2009},}

TY - JOURAU - Caruso, XavierAU - Liu, TongTI - Quasi-semi-stable representationsJO - Bulletin de la Société Mathématique de FrancePY - 2009PB - Société mathématique de FranceVL - 137IS - 2SP - 185EP - 223AB - Fix $K$ a $p$-adic field and denote by $G_K$ its absolute Galois group. Let $K_\infty $ be the extension of $K$ obtained by adding $p^n$-th roots of a fixed uniformizer, and $G_\infty \subset G_K$ its absolute Galois group. In this article, we define a class of $p$-adic torsion representations of $G_\infty $, calledquasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebraic objects. The results of this note should be considered as a first step in the understanding of the structure of quotient of two lattices in a crystalline (resp. semi-stable) Galois representation.LA - engKW - torsion Galois representations; semi-stable representations; norm field theoryUR - http://eudml.org/doc/272378ER -